c2ndps
Functions
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int main(int argc, char *argv[])
c2ndps [ option ] [ infile ]
-m int
order of cepstrum \((0 \le M \le L/2)\)
-l int
FFT length \((2 \le L)\)
infile str
double-type cepstrum
stdout
double-type NDPS
- Parameters
argc – [in] Number of arguments.
argv – [in] Argument vector.
- Returns
0 on success, 1 on failure.
See also
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class sptk::CepstrumToNegativeDerivativeOfPhaseSpectrum
Convert cepstral coefficients to negative derivative of phase spectrum.
The input is the \(M\)-th order cepstral coefficients:
\[ \begin{array}{cccc} c(0), & c(1), & \ldots, & c(M), \end{array} \]and the output is the \((L/2+1)\)-length NDPS:\[ \begin{array}{cccc} n(0), & n(1), & \ldots, & n(L/2+1), \end{array} \]where \(L\) must be a power of two.The log spectrum can be represented as
\[ \log S(\omega) = \sum_{m=0}^{M} c(m) e^{-j\omega m}. \]It can be decomposed into the real part and imaginary part:\[ \log |S(\omega)| + j\arg S(\omega) = \sum_{m=0}^{M} c(m) e^{-j\omega m}. \]By differentiating the equation with respect to \(\omega\), we obtain\[ \frac{\partial}{\partial \omega} \log |S(\omega)| +j \frac{\partial}{\partial \omega} \arg S(\omega) = -j \sum_{m=0}^{M} m \cdot c(m) e^{-j\omega m}. \]From the imaginary part of the above equation, NDPS is obtained as\[ -\frac{\partial}{\partial \omega} \arg S(\omega) = \sum_{m=0}^{M} m \cdot c(m) \cos(\omega m). \]This is equivalent to the real part of the DFT of \(m\,c(m)\):\[ n(k) = \mathrm{Re} \left[ \sum_{m=0}^{M} m \cdot c(m) e^{-j2\pi mk / L} \right]. \]Note that \(c(0)\) is not used in the calculation.[1] B. Yegnanarayana, “Pole-zero decomposition of speech spectra,” Signal Processing, vol. 3, no. 1, pp. 5-17, 1981.
Public Functions
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CepstrumToNegativeDerivativeOfPhaseSpectrum(int num_order, int fft_length)
- Parameters
num_order – [in] Order of cepstrum, \(M\).
fft_length – [in] Length of NDPS, \(L\).
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inline int GetNumOrder() const
- Returns
Order of cepstrum.
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inline int GetFftLength() const
- Returns
FFT length.
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inline bool IsValid() const
- Returns
True if this object is valid.
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bool Run(const std::vector<double> &cepstrum, std::vector<double> *negative_derivative_of_phase_spectrum, CepstrumToNegativeDerivativeOfPhaseSpectrum::Buffer *buffer) const
- Parameters
cepstrum – [in] \(M\)-th order cepstrum.
negative_derivative_of_phase_spectrum – [out] \((L/2+1)\)-length NDPS.
buffer – [out] Buffer.
- Returns
True on success, false on failure.
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class Buffer
Buffer for CepstrumToNegativeDerivativeOfPhaseSpectrum class.
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CepstrumToNegativeDerivativeOfPhaseSpectrum(int num_order, int fft_length)